Closed immersion

For the same-name concept in differential geometry, see immersion (mathematics).

In algebraic geometry, a closed immersion of schemes is a morphism of schemes $f: Z \to X$ that identifies Z as a closed subset of X such that regular functions on Z can be extended locally to X. The latter condition can be formalized by saying that $f^\#:\mathcal{O}_X\rightarrow f_\ast\mathcal{O}_Z$ is surjective.

单词	Closed immersion
释义	Closed immersion 英语百科 Closed immersion For the same-name concept in differential geometry, see immersion (mathematics). In algebraic geometry, a closed immersion of schemes is a morphism of schemes $f: Z \to X$ that identifies Z as a closed subset of X such that regular functions on Z can be extended locally to X. The latter condition can be formalized by saying that $f^\#:\mathcal{O}_X\rightarrow f_\ast\mathcal{O}_Z$ is surjective.
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